Question

You are the Dean of the school of business at St. Anford University. You hire Assistant Professors for a probationary period of seven years, after which they come up for tenure and are either promoted, or turned down, in which case they must find another job elsewhere. The Assistant Professors come in two types: Good (GP) and Exceptional (EP). Any types worse than GP have already been weeded out in the hiring process, but you cannot distinguish between GF and EP. Each individual Assistant Professor knows whether he or she is GP or EP. You would like to tenure only the EP. The payoff from a tenured career at St. Anford is $2 million (think of this as the expected discounted present value of salaries, consulting fees, and book royalties, plus the monetary equivalent of the pride and joy that the faculty member and his or her family would get from being tenured at St Anford.) Anyone denied tenure at St. Anford could get a faculty position at Boondocks College, and the present value of that career is $0.5 million. Your faculty can do research and publish the findings. Each publication requires effort and time and causes strain on the family; all these are costly to the faculty member. The monetary equivalent of this cost is $30,000 per publication for an EP, and $60,000 for a GP. You can set a minimum number of N publications that an Assistant Professor must produce in order to achieve tenure. Questions: (1) Without using any math, describe, as completely as you can, what would happen in a separating equilibrium? (2) There are two potential types of pooling equilibria in this situation. Without any math, describe what they would look like. (3) Now, please go ahead and do the math. What is the set of N that will accomplish your goal of screening EP from GP?

Answer 1